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Practice Solving Consecutive Integer Problems

Site: Saylor Academy
Course: MA007: Algebra
Book: Practice Solving Consecutive Integer Problems
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Date: Tuesday, 15 July 2025, 7:44 AM

Description

Table of contents

Practice Problems

  1. The sum of ‍5 consecutive odd numbers is ‍135.

    What is the second number in this sequence?

  2. The sum of ‍6 consecutive integers is 393.

    What is the second number in this sequence?

  3. The sum of ‍3 consecutive even numbers is 270.

    What is the second number in this sequence?

  4. The sum of ‍4 consecutive integers is 326
    What is the second number in this sequence?

Source: Khan Academy, https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-solving-equations/linear-equations-word-problems/e/integer_sums
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Answers

  1. Call the first number in the sequence \(x\).

    The next odd number in the sequence is \(x+2\).

    The sum of the 5 consecutive odd numbers is:

    \(x+ (x + 2)+ (x + 4)+ (x + 6)+ (x + 8) = 135\)

    \(5x + 20= 135\)

    \(5x = 115\)

    \(x = 23\)

    Since \(x\) is the first number, \(x+2\) is the second odd number.

    Thus, the second number in the sequence is 25.

  2. Call the first number in the sequence \(x\).

    The next integer in the sequence is \(x+1\)

    The sum of the 6 consecutive integers is:

    \(x+ (x + 1)+ (x + 2)+ (x + 3)+ (x + 4)+ (x + 5) = 393\)

    \(6x + 15= 393\)

    \(6x = 378\)

    \(x = 63\)

    Since \(x\) is the first number, \(x+2\) is the third integer.

    Thus, the third number in the sequence is 65.

  3. Call the first number in the sequence \(x\).

    The next integer in the sequence is \(x+2\)

    The sum of the 3 consecutive even numbers is:

    \(x+ (x + 2)+ (x + 4) = 270\)

    \(3x + 6= 270\)

    \(3x = 264\)

    \(x = 88\)

    Thus, the first number is 88.

  4. Call the first number in the sequence \(x\).

    The next integer in the sequence is \(x+1\)

    The sum of the 4 consecutive integers is:

    \(x+ (x + 1)+ (x + 2)+ (x + 3) = 326\)

    \(4x + 6= 326\)

    \(4x = 320\)

    \(x = 80\)

    Since \(x\) is the first number, \(x+1\) is the third integer.

    Thus, the third number in the sequence is 81.